Re: POLARIZATION

[Hugh Logan <hlogan@ix.netcom.com>]

David Abineri wrote:
> I am missing a fundamental point and would welcome clarification if
> possible.
>
> A student asked "When does a polarizing filter stop polarizing if the
> spacing is made greater and greater between the 'strands' in the
> polarizing filter?"
>
> To this I would add; Does a diffracting grating polarize light? (It
> certainly doesn't appear to as we tried in lab).
>
> I believe a clarification concerning polarization would be valuable if
> anyone can help with this issue.
I believe that you might find this discussed in a paperback book, 
_Polarized Light_ by William A. Shurcliff and Stanley S. Ballard
(Van Nostrand Momentum Book No. 7). I think it is out of print, and so
far, I have not found my copy. I think the answer to your question
depends on the relation of the wavelength of the incident light to the
spacing between the strands. In an ordinary diffraction grating with 600
lines per mm, the distance between the rulings is 1670 nm, which is
about three wavelengths for visible light. I believe the book referred
to above mentions an experiment by Bird and Parrish (not the Bird and
Parrish of Boston Celtic fame) in which infrared radiation is incident
on a grid of gold wires. I don't have the data, but I think the
wavelength is considerably longer in proportion to the spacing of the
gold strands. The IR radiation that gets through the grid of gold
strands is polarized with the electric vector pependicular to the
strands, contrary to what the picket fence analogy in some books might
lead one to believe. I believe this is explained on the grounds that
currents are induced in the wires so as to dissipate the energy
corresponding to the components of the vibration of the E vector
parallel to the wires. Similar results have been obtained in a scaled up
version with microwaves. The reference for the experiment with the grid
of gold wires is:
  G. R. Bird and M. Parrish, Jr., J. Opt. Soc. Am._50_, 886 (1960).
I don't have access to it at the moment.
   Ordinary diffraction theory is a scalar theory which doesn't take
into account the electromagnetic nature of the waves. It is valid only
when the aperture dimensions are at least a few wavelengths. There are
more advanced theories which take the electromagnetic and vector nature
of electromagnetic radiation into account, and Maxwell's theory of
electromagnetic waves has been applied directly in some cases. I am
familiar with some experiments with single slit apertures. In ordinary
demonstrations, one might use a slit of width 0.2mm. This is 400
wavelengths for light of wavelength 500 nm. More than thirty years ago,
at the suggestion of the late Dr. Earle K. Plyler of Florida State
University, I observed unpolarized white light through a much narrower
slit. At first I tried a precision adjustable IR spectroscopy slit that
could be adjusted down to 1 micrometer. When this slit width was
approached, one could visually observe a polarization effect, but unlike
in the Bird and Parrish experiment, with the plane of polarization
parallel to the slit. Furthermore, the light appeared more bluish as the
slit narrowed towards 1 micrometer. Further experiments were done with a
V-shaped slit which effectively gave slit widths less than one
micrometer, although we never observed light at less than one
micrometer. We also tried nearly monochromatic polarized and unpolarized
incident light using interference filters and a mercury lamp. Incident
light polarized along the direction of the slit could be observed at
smaller slit widths than light of the same wavelength polarized
perpendicular to the slit. For a given polarization, light of a shorter
wavelength could be observed at a smaller slit width. All this was done
visually.

Hugh Logan